An Inequality with Arctangents in Triangle
$\left(\displaystyle\frac{a^3\cos^3A}{\arctan\frac{1}{2}}+\frac{b^3\cos^3B}{\arctan\frac{1}{5}}+\frac{c^3\cos^3C}{\arctan\frac{1}{8}}\ge\frac{32r^3s^3}{3\pi R^3}\right)$